Question

Solve the inequality$x^2\ge x$and graph the solution set.

Short answer

The solution set of inequality is$\left[-\infty ,0\right]\cup \left[1,\infty \right]$

Step-by-step solution

Step 1. Given Information

The given inequality is$x^2\ge x$

Step 2. Calculation

Solve the inequality by rearranging it such that the right side has 0.

$$\begin{gathered} x^2-x\ge 0 \\ x(x-1)\ge 0 \end{gathered}$$

To determine the real zero, substitute the function equal to zero.

$$\begin{gathered} x(x-1)=0 \\ x=0 \\ or \\ x-1=0\Rightarrow x=1 \end{gathered}$$

Thus, the real number line can be divided into three intervals as follows,

Thus, the solution set of the inequality is$\left[-\infty ,0\right]\cup \left[1,\infty \right]$